[Lemma 4.2 of [1]}]
If \(J \in (X,V)\) , then any \(J\) -holomorphic curve \(u:(\Sigma ,\partial \Sigma ) \rightarrow (X,X \setminus D)\)  satisfies \([u] \cdot _w \ge 0\) .
In particular, \([u]\cdot D \in \operatorname{\mathrm {NE}}\) .


If \(u\)  is not contained inside \(V_q\) , then \(u \cdot V_q \ge 0\)  by positivity of intersection (cf. [2]} or [3]}).
There are \(\ge n+1\)  divisors \(V_q\)  with \([V_q] = [_w]\) , and \(u\)  can't be contained in all of them because their common intersection is empty by transversality.
